Lie bialgebra structures on the Lie algebra $\widetilde{{\mathfrak{sl}}_2(C_q[x,y])}$

Abstract

In the present paper we shall investigate the Lie bialgebra structures on the Lie algebra $\widetilde{{\mathfrak{sl}}_2(C_q[x,y])}$, which are shown to be triangular coboundary.

13 pages